Some stuff you should already know!! Hopefully…. For more practice Ex 6A page 80 – independent study.

Conic Sections Lesson 1 Aims: To get to grips with the basics. To know and recognise the four conic sections and the general forms of their equations. To be able to sketch their graphs using a graphical calculator.

What are conic sections? They are the curves that can be produced by cutting a double c________ along different planes. Different cuts will produce different shaped curves. There are four different ones you need to be familiar with Play 4mins 20 seconds

Angle of cut Uses of parabola

General Equations Type of CurveGeneral EquationSketch Circle Ellipse

General Equations Hyperbola

The Rectangular Hyperbola Where a and b are equal. Asymptotes are at right angles, (y = x and y = -x) the equation reduces to: However more commonly used the 45 0 rotated form : Start with the regular hyperbola formula

Activity Try to match each equation to a graph and label where the graphs cut the x and y axis. Then stick them down to make a poster Do the easy ones first that you recognise. For some of the more complicated ones try subbing in some numbers. Finding out what happens when x or y = 0 may help. Finally try to plot these using your calculator. See below for help! Investigate with your calculator! There is a mode on the calculator for conic sections. (from Menu) This will allow you to draw any of the conic sections. (use INIT from the V-Window F3 key) This could also help you remember the general forms. Using g-solve also allows you to find the key features of the graphs! (intercepts and asymptotes)

Classify and try to sketch each equation. Give as much information as possible. Then add them to your poster!